Global Asymptotic Stability and Nonlinear Analysis of the Model of the Square Immunopixels Array Based on Delay Lattice Differential Equations

On qualitative analysis of the nonstationary delayed model of coexistence of two-strain virus: Stability, bifurcation, and transition to chaos

The model of interaction of two strains of the virus is considered in the paper. The model is based on a nonstationary system of differential equations with delays and takes into account populations of susceptible, first-time and re-infected individuals across two strains. For small values of the delays, the conditions of global asymptotic stability are obtained with the help of Lyapunov functionals technique. In some special cases the exponential estimates are constructed. On the basis of numerical modeling complex chaotic solutions of the model are obtained. Their investigation is performed with help of nonlinear characteristics, namely bifurcation maps based on Poincare sections and the maximal Lyapunov exponent were obtained.